The reason for Russia entering the war was three-fold. One reason was that Russia owed Serbia allegiance, another being the loss of the Russo-Japanese war and the last, and arguably the most important, reason for Russia’s entry is the incompetence of the Czar.
The first reason for Russia entering the war was their allegiance to Serbia. Russia owed Serbia allegiance so when Austria declared was, it was Russia’s duty to fight with Serbia. Russia did this because the Serbians were all Slavophiles. This was important to the Russians as they were Slav as well.
The second reason for Russia entering the World War was the loss of the Russo-Japanese. Nicholas II was the first Russian Czar to lose land instead